A binding problem has been studied that has immediate application to muscle biochemistry and possible future application to binding of ligands on polynucleotides. This is the problem of a linear array of binding sites which are competed for by a monovalent ligand and a divalent ligand. In the most general case, there are nearest-neighbor interactions, though in the muscle problem (myosin fragments bound on actin) interactions seem to be unimportant. Last year we studied the statistical distribution problem, given the binding equilibrium constants. Currently, we are working out the statistical mechanical theory of the equilibrium constants themselves.